Let a- b- c- are three unit vectors of which b- and c- are non parallel- Let the angle between a- and b- be - and that angle between a- and c- be - If a- b-c- -12b- then

The correct option is A α =π2, β =π3 a⃗× ( b⃗×c⃗ )=12b⃗ #160; ⇒ (a⃗.c⃗) b⃗ (a⃗.b⃗) c⃗ = 12b⃗ Comparing the coefficients on both sides of equ ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Let a⃗, b⃗,...

Question

Let $\to a, \to b, \to c$ are three unit vectors of which $\to b$ and $\to c$ are non parallel. Let the angle between $\to a$ and $\to b$ be $α$ and that angle between $\to a$ and $\to c$ be $β$ . If $\to a \times (\to b \times \to c) = \frac{1}{2} \to b$ , then

α = \frac{π}{3}, β = \frac{π}{2}

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α = \frac{π}{2}, β = \frac{π}{3}

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α = \frac{π}{6}, β = \frac{π}{3}

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None of these

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Solution

The correct option is A $α = \frac{π}{2}, β = \frac{π}{3}$
$\to a \times (\to b \times \to c) = \frac{1}{2} \to b$
$\Rightarrow (\to a . \to c) \to b - (\to a . \to b) \to c = \frac{1}{2} \to b$
Comparing the coefficients on both sides of equality, we get $\to a . \to b = 0$ and $\to a . \to c = \frac{1}{2}$
$\Rightarrow cos α = 0$ and $cos β = \frac{1}{2}$
$\Rightarrow α = \frac{π}{2}$ and $β = \frac{π}{3}$

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Similar questions

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Let →a,→b,→c are three unit vectors of which →b and →c are non parallel. Let the angle between →a and →b be α and that angle between →a and →c be β. If →a×(→b×→c)=12→b, then

The correct option is A α=π2,β=π3→a×(→b×→c)=12→b ⇒(→a.→c)→b−(→a.→b)→c=12→bComparing the coefficients on both sides of equality, we get →a.→b=0 and →a.→c=12⇒cosα=0 and cosβ=12⇒α=π2 and β=π3

Let $\to a, \to b, \to c$ are three unit vectors of which $\to b$ and $\to c$ are non parallel. Let the angle between $\to a$ and $\to b$ be $α$ and that angle between $\to a$ and $\to c$ be $β$ . If $\to a \times (\to b \times \to c) = \frac{1}{2} \to b$ , then